{
  "id": "1901.03841",
  "version": "v1",
  "published": "2019-01-12T10:29:27.000Z",
  "updated": "2019-01-12T10:29:27.000Z",
  "title": "Diophantine equations coming from binomial near-collisions",
  "authors": [
    "Nikos Katsipis"
  ],
  "comment": "27 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we solve the Diophantine equation $\\binom{m}{l}-\\binom{n}{k}=d$ (where m,n are positive integers unknowns) when (k,l)=(3,6) for various values of d and when (k,l)=(8,2) and d=1. As a byproduct of our results we will obtain that (k,l)-near collisions with difference 1 do not exist if (k,l)=(6,3), (3,6), (8,2) thus establishing a conjecture stated in the article \"Binomial collisions and near collisions\" published by A. Blokhuis, A. Brouwer and B. de Weger in Integers 17 (2017), A64.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-12T10:29:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "diophantine equations coming",
      "binomial near-collisions",
      "binomial collisions",
      "positive integers unknowns",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}